A group of physicists suggests humans follow particular rules while interacting in crowds:

Skinner and his coauthors, a pair of computer scientists at the University of Minnesota, looked at six data sets that capture individual movements in crowded places: four from natural settings, like video footage of pedestrians on a college campus, and two from laboratory experiments, in which participants were tracked with cameras as they navigated a corridor that narrowed into a bottleneck. Such data sets have become available only in the last five years, as improvements in camera technology and the field of computer vision have made large-scale pedestrian tracking possible.

Initially the researchers assumed they would find a “repulsive force” between people, like the one that pushes charged particles apart. As they looked closer, they realized it wasn’t that simple: There was a repulsive force between individuals, but it only operated sometimes. “Two people walking head first into each other have a strong interaction,” Skinner says, “but people walking side-by-side have almost no interaction.”

So the researchers went looking for a new rule. They found it in a variable they called “time to collision,” which explained many of the course adjustments they observed. The closer two people get to colliding, the more energy they expend getting out of each other’s way. To be technical, they found that the interaction between individuals in a crowd could be described as 1 over the square of the time to collision: As a collision becomes more imminent, the energy you apply to avoiding it goes up drastically.

Unlike with particles, the mechanism that produces these adjustments is an instinctive mental calculation rather than any kind of physical force. There’s also a limit to how far out we can—or need—to account for other people’s movement. When the time to collision was more than three seconds, the researchers found that the interaction energy between two pedestrians fell to zero, meaning people weren’t taking each other into account at all.

This seems to apply mainly to areas where people are going opposite directions, whether in an open concourse at a stadium or a crowded city crosswalk with two masses of people trying to get past each other. In these situations, there is usually an area of stronger flow on each side but then in the middle – between the two larger flows – is a zone where such collisions are imminent. I know because I often walk in such zones when in a hurry. It can be difficult in those situations to avoid people and not everyone likes to walk in such high-stakes areas where there is a higher probability of bumping into people.

The article goes on to talk about applications of these findings. I would guess that means having more clearly marked traffic flows and trying to avoid the weaker flows or neutral areas that I mentioned.